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Toolbox

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  • Matlab Toolbox for self DDE calibration in radio interferometric imaging

    Download : GitHub

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    The code made available here represents a proof of concept MATLAB implementation of the proposed algorithm, for self-calibration of direction-dependent effects (DDEs) in radio interferometric imaging.

    Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magnitude. At this precision level, the direction-dependency of the gains must be accounted for, and radio interferometric imaging can be understood as a blind deconvolution problem. In this context, the underlying minimization problem is non-convex, and adapted techniques have to be designed.
    In this toolbox, leveraging recent developments in non-convex optimization, we propose the first joint calibration and imaging method in radio interferometry, with proven convergence guarantees. Our approach, based on a block-coordinate forward-backward algorithm, jointly accounts for visibilities and suitable priors on both the image and the DDEs. As demonstrated in recent works, sparsity remains the prior of choice for the image, while DDEs are modelled as smooth functions of the sky, i.e. spatially band-limited.

    Related articles:
    • A. Repetti, J. Birdi, A. Dabbech, and Y. Wiaux, Non-convex optimization for self-calibration of direction-dependent effects in radio interferometric imaging. Monthly Notices of the Royal Astronomical Society, vol. 470, no. 4, pp. 3981-4006, Oct. 2017. [pdf]
    • A. Repetti and Y. Wiaux, A non-convex perspective on calibration and imaging in radio interferometry. In Proceedings of the conference on Wavelets and Sparsity XVII, part of the SPIE Optical Engineering + Applications, San Diego, California, United States, 6-9 August 2017. [pdf]
    • A. Repetti, J. Birdi, and Y. Wiaux, Non-convex blind deconvolution approach for sparse radio-interferometric imaging. In Proceedings of the Signal Processing with Adaptive Sparse Structured Representations (SPARS 2017), Lisbon, Portugal, 5-8 June 2017. [pdf] [poster]
    • A. Repetti, J. Birdi, and Y. Wiaux, Joint imaging and DDEs calibration for radio interferometry. In Proceedings of international Biomedical and Astronomical Signal Processing (BASP) Frontiers workshop, page 25, Villars-sur-Ollon, Suisse, 29 Janvier-3 Février 2017. [pdf]
    • E. Chouzenoux, J.-C. Pesquet and A. Repetti, A Block Coordinate Variable Metric Forward-Backward Algorithm. J. Global Optim, vol. 66, no. 3, pp. 457-485, Nov. 2016. [pdf]


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  • Matlab Toolbox for SOOT algorithm: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization

    Téléchargement : RestoVMFB_Lab_v1.0.zip

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    This Matlab toolbox is designed to reconstruct a sparse seismic signal x, from the degraded observation model y=h*x+w, where h is an unknown convolution kernel and w ia a realization of a white Gaussian noise.
    In the context of blind deconvolution problems, the regularization term l1/l2 is known to be particularly suitable to reconstruct sparse signals.
    In the article associated with toolbox, a smooth approximation of this regularization term is proposed. The resulting non-convex minimization problem is then solved leveraging a variable block-coordinate forward-backward algorithm.

    Related articles:
    • E. Chouzenoux, J.-C. Pesquet and A. Repetti, A Block Coordinate Variable Metric Forward-Backward Algorithm. J. Global Optim, vol. 66, no. 3, pp. 457-485, Nov. 2016. [pdf]
    • A. Repetti, M. Q. Pham, L. Duval, E. Chouzenoux and J.-C. Pesquet, Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization. Signal Processing Letters., vol. 22, no. 5, pp. 539-543, May 2015. [pdf] [poster at ICASSP 2015]


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  • Matlab Toolbox for image restoration using the VMFB algorithm

    Téléchargement : RestoVMFB_Lab_v1.0.tar.gz, RestoVMFB_Lab_v1.0.zip

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    This Matlab toolbox can be used to estimate an image degraded by a linear operator, and corrupted by an additive signal-dependent Gaussian noise.
    Using a maximum a posteriori approach, this problem is solved by minimizing a penalized criterion G = F + R, where F is the data-fidelity term corresponding to the forward model (corresponding to the negative log-likelihood associated with the noise), and R is the regularization term incorporating prior information on the target solution (in the toolbox corresponding to the indicator function of a convex - to constraint the amplitude of the estimated image pixels - and an isotropic total variation term).
    To minimize the function G, a variable-metric forward-backward algorithm is leveraged. The variable metric is used to accelerate the convergence of the usual forward-backward algorithm, and is chosen using a majorization-minimization strategy.

    Related articles:
    • E. Chouzenoux, J.-C. Pesquet and A. Repetti, Variable Metric Forward-Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function. J. Optim. Theory and Appl., vol.162, no. 1, pp. 107-132, Jul. 2014. [pdf]
    • A. Repetti, E. Chouzenoux and J.-C. Pesquet, Reconstruction d'image en présence de bruit gaussien dépendant par un algorithme Explicite-Implicite à métrique variable. In Actes du 24e colloque GRETSI, Brest, France, 3-6 septembre 2013. [abstract] [pdf] [slides]


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Contact

Biomedical and Astronomical Signal Processing group
Institute of Sensors, Signals and Systems
Heriot-Watt University
Edinburgh EH14 4AS
UK

mail: A.Repetti@hw.ac.uk

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